1. Field of the Invention
The present invention relates to a geometric modeling method and an apparatus therefor capable of inputting a two-or three-dimensional shape in a computer or the like to form a shape and a scale, and performing changing (cancelling, adding, and correction) of the shape or scale.
2. Description of the Related Art
The following literatures can be referred to as materials describing relevant techniques in detail.
(1) Y. Yamaguchi, F. Kimura & P. J. W. ten Hagen, "INTERACTION MANAGEMENT IN CAD SYSTEMS WITH HISTORY MECHANISM" EUROGRAPHICS '87, 1987.
(2) R. Light & D. Gossard, "Modification of geometric models through variational geometry", Computer-Aided Design, Vol. 14, No. 4, July 1982.
(3) B. Aldefeld, "Variation of geometries based on a geometric-reasoning", Computer-Aided Design, Vol. 20, No. 3, April 1988.
Conventionally, geometric models such as a wire-frame model, a surface model, and a solid model are used to input a two- or three-dimensional shape in a computer or the like. The wireframe model is a method of expressing a shape only by edges like a wirework. The surface model is a method of expressing a three-dimensional shape as an aggregation of its faces. The solid model is a method of expressing a three-dimensional shape including a difference between the interior and exterior of a solid into a computer. More specifically, in a known method of expressing a three-dimensional shape, faces and a relation between the faces are expressed by a relation between edges and faces and a relation between edges and points, thereby expressing how the faces are connected to form the surface of the solid (by, e.g., using an equation representing a predetermined shape or performing point-and-vector (normal vector) display), and describing which side of each face is inside the solid.
These methods, however, aim at correctly expressing the shape of a solid in a computer. That is, a computer stores only the final shape of an input shape. Therefore, in order to correct the shape, a new shape must be formed, or the type of changing must be specified for all of shape elements such as a face, an edge, and a point to be changed upon correction. For example, even if there is only one portion to be corrected, a large number of portions must be corrected upon correction of the one portion. That is, since all the portions must be corrected in order to achieve perfect correction, a correction operation becomes very cumbersome.
In order to solve the above problem, a method has been proposed in which relations between faces o edges of a solid or equations to be satisfied are independently defined (e.g., a relation between coordinates and a distance in a space is defined as an equation, or a parallel or perpendicular relation between faces or edges is defined), and the shape is deformed on the basis of this information. In these methods, however, since additional information must be added (after shape formation) to a geometric model formed beforehand, an operation of forming the adding information becomes cumbersome. For example, in the case of a triangle as shown in FIG. 35, conditions to be satisfied by this shape are six simultaneous equations f1 to f6 shown on the left side of FIG. 35. In this case, even if one of the equations is not satisfied or another condition is added, the solution cannot be obtained. That is, a shape cannot be uniquely determined unless adding information is formed without any addition or omission.
As described above, it is difficult to cope with changing of a shape by only a geometric model. In addition, in order to realize shape changing, adding information must be independently added without any addition or omission. It is very difficult to independently define adequate adding information without any addition or omission for a corresponding partial shape such as a circle, a line segment, or a vertex of interest of a general complicated shape. In addition, since adding information must be independently formed for each partial shape, this conventional method has no sufficient versatility and therefore is not practical.